A population consist of five (5) measurements 2,3,5,6 and 7. What is the variance of the sampling distribution?

Question

A population consist of five (5) measurements 2,3,5,6 and 7. What is the variance of the sampling distribution?

a.

0.89

b.

1.29

c.

3.90

d.

2.20

Answer 1

2,3,5, 6 & 7 have a mean = 23/5= 4.6

2-4.6 = -2.6. 2.6^2 = 6.76

3-4.6 = -1.6 1.6^2 = 2.56

5-4.6 = .4 .4^2 =.16

6-4.6 = 1.4 1.4^2 = 1.96

7-4.6 =2.4 2.4^2 = 5.76

sum of squared deviations from the mean =17.2

17.2/5 = 3.44 = variance

standard deviation = sqr3.44 = 1.84

another method is sum the squares of each measurement, 2^2 + 3^2 + 5^2 + 6^2 + 7^2 = 123

divide by 5 to the avege = 24.6

subtract the mean squared = 4.6^2 = 21.16

24.6 - 21.16 = 3.44= variance

UNLESS this was from a sample and not the population, then divide by n-1 =4

17.2/4 = 4.3 = variance

standard deviation = sqr4.3 = about 2.08